2007
(a) Find, correct to one decimal place, the angle between \(p = \begin{pmatrix} 3 \\ -1 \end{pmatrix}\) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\).(b) ABCD is a square with vertices at A(0, 0), B(2, 0), C(2, 2) and…
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2007 WAEC SSCE Further Mathematics Past Questions
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2007
The table shows the marks obtained by some candidates in Physics (y) and Mathematics (x) tests.Mathematics43464839306084540Physics545363304475203349(a)(i) Represent this information on a scatter diagram.(ii) Find \(\bar{…
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2007
The table below shows the distribution of ages of workers in a company.Age/ yr17 - 2122 - 2627 - 3132 - 3637 - 4142 - 4647 - 5152 - 56Workers122430374525107(a) Using an assumed mean of 39, calculate the (i) mean (ii) sta…
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2007
(a) If \(^{18}C_{r} = ^{18}C_{r + 2}\), find \(^{r}C_{5}\).(b) In a community, 10% of the people tested positive to the HIV virus. If 6 persons from the community are selected at random, one after the other with replacem…
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2007
(a) Using the trapezium rule with seven ordinates, evaluate \(\int_{0}^{3} \frac{\mathrm d x}{x^{2} + 1}\), correct to two decimal places.(b) Using matrix method, solve \(-2x + y = 3; - x + 4y = 1\).
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2007
(a) Given that \(\begin{vmatrix} 5 & 2 & -3 \\ -1 & k & 6 \\ 3 & 9 & (k + 2) \end{vmatrix} = -207\), find the values of the constant k.(b) The equation of a curve is \(x(y^{2} + 1) - y(x^{2} + 1)…
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2007
(a) Solve the equation : \(\sqrt{4x - 3} - \sqrt{2x - 5} = 2\).(b) Find the finite area enclosed by the curve \(y^{2} = 4x\) and the line \(y + x = 0\).
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2007
(a) The roots of the equation \(x^{2} + mx + 11 = 0\) are \(\alpha\) and \(\beta\), where m is a constant. If \(\alpha^{2} + \beta^{2} = 27\), find the values of m.(b) The line \(2x + 3y = 1\) intersects the circle \(2x^…
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2007
An object is projected vertically upwards. Its height, h m, at time t seconds is given by \(h = 20t - \frac{3}{2}t^{2} - \frac{2}{3}t^{3}\). Find (a) the time at which it is momentarily at rest (b) correct to two decimal…
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2007
Forces \(F_{1} = (10 N, 090°), F_{2} = (20 N, 210°)\) and \(F_{3} = (4 N, 330°)\) act on a body at rest on a smooth table. Find, correct to one decimal place, the magnitude of the resultant force.
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2007
Four boys participated in a competition in which their respective chances of winning prizes are \(\frac{1}{5}, \frac{1}{4}, \frac{1}{3}\) and \(\frac{1}{2}\). What is the probability that at most two of them win prizes?
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2007
Five digit numbers are formed from digits 4, 5, 6, 7 and 8.(a) How many such numbers can be formed if repetition of digits is (i) allowed (ii) not allowed?(b) How many of the numbers are odd, if repetition of digits is n…
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2007
(a) Write down the first four terms of the binomial expansion of \((2 - \frac{1}{2})^{5}\) in ascending powers of x.(b) Use your expansion in (a) above to find, correct to two decimal places, the value of \((1.99)^{5}\).…
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2007
The normal to the curve \(y = 2x^{2} + x - 3\) at the point \((2, 7)\) meets the x-axis at the point P. Find the coordinates of P.
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2007
Solve \(x^{\frac{2}{3}} - 5x^{\frac{1}{3}} + 6 = 0\).
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2007
The second term of a geometric progression is 3. If its sum to infinity is \(\frac{25}{2}\), find the value of its common ratio.
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2007
Three forces \(F_{1} = (8 N, 300°), F_{2} = (6 N, 090°)\) and \(F_{3} = (4 N, 180°)\) act on a particle. Find the vertical component of the resultant force.
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2007
A force of 30 N acts at an angle of 60° on a body of mass 6 kg initially at rest on a smooth horizontal plane. Find the distance covered in 10 seconds.
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2007
A group of 5 boys and 4 girls is to be chosen from a class of 8 boys and 6 girls. In how many ways can this be done?
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2007
Calculate, correct to one decimal place, the standard deviation of the numbers: -1, 5, 0, 2 and 9.
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